Amodu had been given official backing in Angola during the Nations Cup by the federation's board as the pressure began to mount, but a stormy meeting in Abuja that went late into the night on Friday sealed his fate.
It is the second time Amodu has been removed from his post heading into a World Cup finals tournament.
"The decision was taken during the board meeting," said Nigeria Football Federation media officer Idah Peterside.
"The technical committee of the federation has been mandated to have a new man in place by the end of the month."
Others in the frame are former England caretaker manager Peter Taylor, Bruno Metsu, who coached Senegal to the 2002 World Cup quarter-finals, and Ratomir Dujkovic, Ghana's coach at the last World Cup in Germany.
Nigeria reached the semi-finals at this year's tournament but lost to an under-strength Ghana. The Super Eagles were also beaten by Egypt in their opening group game and needed penalties to overcome Zambia in the quarter-finals.
Amodu will take charge of Nigeria's home-based players for the African Nations Champions tournament, a tournament recently introduced for players who play their club football on the continent, Peterside said.
"He will be in charge of talent identification and finding players for the future."
